A metal oxide semiconductor field effect transistor (MOSFET) device is a semiconductor device in which a gate dielectric layer electrically insulates a channel region of a semiconductor body from an overlying gate electrode. The channel region extends between a source region and a drain region of the transistor. The substrate region or the substrate (sometimes referred to as the body) is manufactured having an opposite conductivity type than the source and drain.
The charge carriers for an n-channel MOSFET are electrons. The charge carriers for a p-channel MOSFET are holes. The charge carriers move from the source region through the channel region to the drain region when appropriate voltages are applied to the gate electrode, and to the source region and to the substrate region.
Substrate doping density (designated Na) is a key parameter that affects the on and off states of a MOSFET device. Due to the importance and widespread use of MOSFET devices in the integrated circuit (IC) industry, several prior art methods have been proposed that measure the substrate doping density Na. The measured value of the substrate doping density Na in turn predicts the characteristics and operating performance of the MOSFET devices.
One prior art method is the electromechanical capacitance-voltage method (sometimes referred to as the ECV method). The ECV method is based upon an analysis of the capacitance-voltage characteristics of metal oxide semiconductor (MOS) capacitance. The ECV method is described in a book by Dieter K. Schroder entitled “Semiconductor Material Device Characterization”, Second Edition, pp. 79-82, John Wiley & Sons, New York, 1990.
The ECV method determines the substrate doping density Na by electrolytically etching the semiconductor between capacitance measurements. However, the ECV method is destructive because it etches a hole in the semiconductor sample. For MOSFET devices, the polysilicon and the gate oxide layers have to be removed before beginning to perform the ECV method. Furthermore, following the well and channel implant procedures, MOSFET devices will often experience additional manufacturing steps such as Lightly Doped Drain (LDD) implant steps and high temperature deposition steps. These additional manufacturing steps make the substrate doping density Na appear to have different values compared to the substrate doping density Na of a MOSFET capacitor.
A second prior art method determines the doping profile in epitaxial layers of semiconductor devices. This method measures the conductivity variation originated from a photocurrent that is generated by a laser beam striking an epitaxial layer of the device. This method is described in U.S. Pat. No. 4,456,780 issued to Hans P. Kleinknecht on Jun. 26, 1984. However, the Kleinknecht method is inconvenient and inaccurate for MOSFET devices.
A third prior art method for measuring the substrate doping density Na of MOSFET devices utilizes the relationship between MOSFET threshold voltage (VTH) and the source to substrate (body) bias voltage (VSB). For a MOSFET device with a bias voltage VSB applied between the source and the substrate, the threshold voltage VTH is given by the expression:VTH=VTO+λ(√{square root over (VSB+φS)}−√{square root over (φS)})  Eq. (1)
where VTO is the threshold voltage when VSB is zero and where φS is the surface potential. The coefficient λ is the body-bias coefficient that is determined by the expression:
                    λ        =                                            2              ⁢                              ɛ                SI                            ⁢                              qN                a                                                          C            OX                                              Eq        .                                  ⁢                  (          2          )                    
where the expression COX is the gate oxide capacitance. The value of the gate oxide capacitance COX is readily available for the device being tested using well-established capacitance-voltage measurements or inline gate oxide thickness measurements. The substrate doping density is represented by the expression Na. The expression ∈SI represents the permittivity of silicon. The letter q represents the charge of an electron.
A linear relationship exists between the threshold voltage VTH and the expression √{square root over (VSB+φS)}−√{square root over (φS)}. Therefore, the third prior art method is able to obtain a value for the substrate doping density Na by using the following procedure:
1. Measure VTH using different values of VSB.
2. Generate a set of data points of VTH versus
√{square root over (VSB+φS)}−√{square root over (φS)} using an estimated value of φS.
3. Plot the data points on a graph to determine the linear relationship between VTH and √{square root over (VSB+φS)}−√{square root over (φS)}.
4. Draw a best fit straight line through the plotted values of VTH versus the values of √{square root over (VSB+φS)}−√{square root over (φS)}.
5. Calculate the y-intercept VTO and the slope λ.
6. Then calculate the value of the substrate doping density Na by placing the value of λ in Equation (2) and solving Equation (2) for the value of Na.
This third prior art method treats the value of the surface potential φS as a constant. This constant φS is taken to be approximately seven tenths of a volt (0.7 V).
In reality the value of the surface potential φS actually depends upon the value of the substrate doping density Na in accordance with the following relationship:
                              ϕ          S                =                  2          ⁢                      kT            q                    ⁢                      ln            (                                          N                a                                            n                i                                      )                                              Eq        .                                  ⁢                  (          3          )                    
where the letter k represents the Boltzmann constant, and the letter T represents the temperature, and letter q represents the charge of an electron, and the expression ni represents the intrinsic carrier density in silicon.
The prior art methods that determine the value of the substrate doping density Na by assuming a constant value for the surface potential φS are bound to create erroneous results. This is because the surface potential φS is actually dependent on the value of the substrate doping density Na (as seen in Equation (3)).
Therefore, there is a need in the art for a system and method that is capable of obtaining a precise and accurate measurement of substrate doping density Na in a MOSFET device. In particular, there is a need in the art for a system and a method that can obtain more precise and accurate measurements of substrate doping density Na in a MOSFET device by taking into account the fact that the value of the surface potential φS is not a constant but is dependent on the value of the substrate doping density Na of the MOSFET device.